By comparison, stocks have no property taxes, and profits are taxed at a lower capital gains rate.
True, no property taxes on stocks. But you can't defer income via depreciation either. Please explain the part about profits from stocks taxed at a lower capital gains rate (than real estate). Real estate (and actively trading stocks for that matter) can have big tax consequences/advantages. Your statement makes me think you should thoroughly research the tax implications of all options before proceeding.
My question is, should I focus on real estate, or just put things into a mixture of safe dividend stocks?
As Alex said, there's no reason to make this all or none. Even if you have the capital and the credit to jump into real estate in a big way, it just makes sense to wade in at first. With your "significant savings" you will be able to ramp up your holdings quickly if that path proves worthwhile.
My advice?
a) Get out of your individual stocks as soon as you can without incurring short-term capital gains and get into one or more index funds that represent a diverse set of asset classes.
b) educate yourself on the tax consequences of realizing gains from stock trading and the tax consequences/benefits of owning residential real estate for rental. Specifically, download a Schedule E and start filling it out using a hypothetical real estate investment. See how it would effect your taxes. Don't proceed until you are comfortable with your estimate for each line item on your hypothetical Schedule E.
c) if you are still interested in real estate, explore your options for exit strategies, including the tax consequences of those exit strategies. At a minimum, understand what a 1031 Exchange is and what depreciation recapture is. Also be aware of the different tax consequence depending on which tax bracket you are in when you sell/exchange.
d) if you are still interested in real estate, become at least somewhat familiar with landlord tenant laws, customs, and common mistakes and problems.
e) if you are still interested in real estate, buy one place and see how it goes. Give it plenty of time (at least 1 or 2 tax filings) to see how things are shaking out before you buy another.
f) Whether you do your own taxes or not, pay close attention to how your real estate investment is affecting your income, taxes, net worth.
g) providing you have a personal emergency fund, an operating fund for the rental property, put everything in index funds until you want to start a more liquid pool for a down payment on another property.